On the Lebesgue structure of the distribution of a random variable defined by continued A2-fractions
Abstract
In this paper, we study the Lebesgue structure of the distribution of a random variable given in terms of a continued fraction with a two-symbol alphabet \12, 1\, also known as A2-fractions. We establish necessary and sufficient conditions for the distribution to be discrete and provide some sufficient conditions for its singularity. We also explore non-trivial metric properties of the A2-representation with the specified alphabet.
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